Dates are a bit off, and there are only four children, but:
Sailing from Liverpool to New Orleans, Louisiana on board the Sciota, arriving 28 April 1851
Wm Barber, age 40, Labourer
Charles, age 60, Labourer
Maria(?), age 34
William, age 13
Elizabeth, age 9
Henery(?), age 7
Charles, Inft